Apparatuses of the type described above are used, inter alia, in order to cut a railroad rail at right angles to the longitudinal direction of the rail. The securing device in this case consists of a screwy vice which is mounted on the rail. In these apparatuses it is normal for the holder with the arm, which is referred to above as the rear arm, to be connected to the machine at a hinge, rotatable about an axis of rotation outside the rear edge of the cutting wheel. Such an apparatus is described, for example, in U.S. Pat. No. 3,974,596. In order to be able to mount the machine in such a way that the cutting wheel can move free from the rail, the arms must have a considerable length. Their considerable length also means that they have to be made robust in order to exhibit sufficient bending rigidity. The considerable length and the robust construction in turn mean that the whole holder is heavy. The weight alone means that it is therefore difficult to carry the machine with the holder mounted on the machine. In addition, with the said long arms, the holder drags along the ground if the machine is carried in the normal way by a person of normal height. These circumstances mean that it is necessary in practice to detach the holder from the machine before transporting it over any appreciable length, so that it can be carried as two separate loads, and thereafter to secure the holder again on the machine. It will be understood that this is laborious and constitutes a considerable disadvantage in apparatuses of the known type which has been described.